A047020 - OEIS

A047020

Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no step touches the line y=2x/3 unless x=0 or x=h.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 4, 5, 4, 3, 1, 1, 5, 9, 5, 3, 4, 1, 1, 6, 14, 14, 5, 7, 5, 1, 1, 7, 20, 28, 19, 7, 12, 6, 1, 1, 8, 27, 48, 47, 19, 19, 18, 7, 1, 1, 9, 35, 75, 95, 66, 38, 37, 25, 8, 1, 1, 10, 44, 110, 170, 161, 66, 37, 62, 33, 9